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JEE Advanced2023ChemistrySolid StateActual

Atoms of metals x , y and z form face-centred cubic (fcc) unit cell of edge length L x , body-centred cubic (bcc) unit cell of edge length L y , and simple cubic unit cell of edge length L z , respectively. If r z = 3 2 r y ; r y = 8 3 r x ; M z = 3 2 M y and M z = 3 M x , then the correct statement(s) is(are) [Given: M x , M y , and M z are molar masses of metals x , y , and z , respectively. r x , r y , and r z are

Options

  1. APacking efficiency of unit cell of x > Packing efficiency of unit cell of y > Packing efficiency of un
  2. BL y > L z
  3. CL x > L y
  4. DDensity of x > Density of y

Correct answer

A. Packing efficiency of unit cell of x > Packing efficiency of unit cell of y > Packing efficiency of un

Step-by-step solution

Metal x forms FCC (edge length L x ) Metal y forms BCC (edge length L y ) Metal z forms SC (edge length L z ) Given r z = 3 2 r y and r y = 8 3 r x ∴    r z = 3 2 × 8 3 r x = 4 r x M z = 3 2 M y    M z = 3 M x ∴ M y = 2 M x Packing efficiency FCC   >   BCC   >   SC Packing efficiency unit cell x > y > z In FCC unit cell:- atoms along the face diagonals are in contact. ∴ 2   L x = 4 r x ⇒ L x = 2 2 r x In BCC unit cell: atoms a

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